A cloud-based service included in Microsoft 365, delivering scalable messaging and collaboration features with simplified management and automatic updates.
New ones will be created as you bring up new servers and databases, no need to migrate any of those.
They will be removed when you remove the old databases and servers.
You can remove the old ones with powershell, yes
You can delete them all with powershell:
Get-Mailbox -Monitoring -Database <OLD DB> | Remove-Mailbox
Make sure you also read this and give the necessary permissions so the AD objects are removed:
https://learn.microsoft.com/en-us/exchange/troubleshoot/administration/remove-mailboxdatabase-cannot-remove-health-mailboxes
Otherwise, remove the specific AD objects manually from the Monitoring container
Even if you screw up and remove the wrong ones, its ok.
Simply restart the Microsoft Exchange Health Manager, MSExchangeHM service on each new server if that happens to recreate them